As is known, in the recent past the need for more and more reliable localization systems has been more and more felt.
Consequently, many localization systems designed to determine or track users' position have been proposed over the years.
The localization systems can be divided into three main categories: global location systems, wide-area location systems based on cellular networks, and indoor location systems.
A typical global location system is the Global Positioning System (GPS), which exploits signals from multiple satellites to perform a multilateration process in order to determine locations with an accuracy of approximately 5 m. However, GPS is inefficient for indoor use or in urban areas where high buildings shield the satellite signals, i.e. in deep indoor conditions.
On the other hand, cellular-network-based wide-area location systems, generally, are based on measuring signal strengths to know the distance between a user terminal and a base station. However, the accuracy of wide-area location systems is highly limited by the cell size. Moreover, the effectiveness of these systems for an indoor environment is also limited by multiple reflections suffered by the radio frequency (RF) signal, which cause, for instance, multipath and shadowing phenomena.
Finally, indoor location systems are just designed to perform localization in indoor environments. Several indoor location systems based on various technologies, such as infrared (IR), ultrasound, video surveillance, and RF signal, have been proposed over the year. Among these systems, RF-based approaches have obtained great attention in recent years because RF-based localization systems have distinct advantages in indoor environments over all other systems.
In fact, an RF-based localization system is a low cost solution and covers a large area compared with other types of indoor location systems. Indeed, an RF-based localization system may work in a large building or even across many buildings.
Furthermore, an RF-based localization system is a stable system owing to its robust RF signal propagation, contrary to video- or IR-based location systems which are subject to restrictions, such as line-of-sight limitations or poor performance with fluorescent lighting or in direct sunlight.
Typical RF-based localization systems exploit Wireless Fidelity (Wi-Fi) systems, i.e. based on IEEE 802.11 standard, as well as other wireless systems, such as Wireless Sensor Networks, Bluetooth-based networks etc.
In fact, generally, an RF-based localization system for an indoor environment comprises an RF transmitting node network, such as a WiFi network, comprising a plurality of RF transmitting nodes, such as typical access points, arranged within the indoor environment and configured to transmit respective RF signals over a single radio channel. The RF-based localization system further comprises at least an electronic mobile device, such as a laptop or a palmtop, which is to be located within the indoor environment. The electronic mobile device is configured to receive the RF signals from the RF transmitting nodes over the single radio channel.
Generally, the localization of the electronic mobile device performed by the RF-based localization systems is based on Received Signal Strength (RSS) approach, which refers to a known technique according to which electronic mobile device's location within the indoor environment is estimated by comparing a current received signal strength fingerprint with stored reference signal strength fingerprints.
The general philosophy of the RSS approach is to establish a one-to-one correspondence between a given position and the mean signal strength received in that given position from the RF transmitting nodes.
In detail, the RF-based localization systems needs to be trained before performing the localization of the electronic mobile device. Accordingly the localization process comprises two main phase:                a training phase, wherein mean powers of the RF signals received from the RF transmitting nodes over the single radio channel are computed in reference positions and inserted into an RF database to create an RF map of the indoor environment, the RF map containing reference signal strength fingerprints in the reference positions; and        an online phase, wherein the electronic mobile device to be located computes current powers of the RF signals received in its location within the indoor environment from the RF transmitting nodes over the single radio channel, and then compares the current powers with all tuples of the RF database to select that reference position of the RF map which is closer in terms of received power.        
The RF map is organized as an array wherein each row refers to the powers of the RF signals received in a corresponding reference position from the RF transmitting nodes, each of them indexing one column of the array.
Once the electronic mobile device has computed the current powers of the RF signals received from the RF transmitting nodes and it has formed with those current powers a corresponding current power vector, it compares this current power vector with all the rows of the RF map in order to find the closest match.
Comparing is normally based on an Euclidean distance between the current power vector and each row of the RF map so that the electronic mobile device is located in that reference position whose corresponding row in the RF map has the smallest Euclidean distance from the current power vector.